Chapter 7. Summary, Conclusions, and Recommendations

SUMMARY

This report presents the results of a study that uses
forwardcalculation techniques to screen the backcalculated computed
parameter files in the LTPP database. The two different
forwardcalculation techniques developed appear to produce
reasonable results, both for screening and for estimates of
moduli—one for the subgrade and one for the bound surface course
layer. In addition, for flexible pavements a relationship developed
by Dorman and Metcalf was used for estimates of the modulus of the
unbound base course(s). For rigid pavements, a set of ratios
relating the modulus of the concrete layer to the base layer was
used, very similar to the method in part of the LTPP database
covering backcalculation of rigid pavement systems.

The entire set of computed parameter tables of backcalculated
pavement layer data was screened with appropriate forwardcalculated
moduli. These data cover all available AC and PCC sections where
backcalculation was carried out, including both level E and
nonlevel E (Release 16.0—All QC Levels, July 2003 Upload). These
computations were divided into two parts: a layered-elastic
backcalculation approach using the MODCOMP computer program and a
backcalculation approach developed specifically for rigid pavement
systems using slab-on-dense-liquid and slab-on-elastic solid
theory.

Some percentage of the backcalculated flexible pavement layered
elastic moduli in the LTPP database derived from MODCOMP were
assumed, or fixed, based on engineering judgment and to facilitate
the backcalculation process. These values were not screened, but
rather left unchanged as they exist in the existing tables with an
associated “Y” flag. An even larger percentage of the
backcalculated (and some of the forwardcalculated) data were
considered to be not within a reasonable range according to the
values presented in Table 14. For
easy reference, this table is reproduced in this section as
Table 17. Records containing moduli
outside of the ranges shown in Table 17 were
not further screened. Instead, they were flagged (using an “N” data
cell, as appropriate) as not reasonable. All remaining records were
then screened using the corresponding forwardcalculated moduli.
Four different correspondence flags associated with each screened
data record have been designated (see Table 15):

0

=

Acceptable: The backcalculated value is within
a factor of 1.5 of the forwardcalculated value.

1

=

Marginal: The backcalculated value is within a
factor of 2.0 of the forwardcalculated value (not 0).

2

=

Questionable: The backcalculated value is
within a factor of 3.0 of the forwardcalculated value (not 0 or
1).

3

=

Unacceptable: The backcalculated value is
greater than 3 times or less than ? times the forwardcalculated
value.

Table 17. Reasonable ranges for various pavement layers in
the LTPP database (same as Table 14).

By and large, the screening process produced a set of excellent
relationships for the rigid pavement data, essentially based on
two-layer slab-on-elastic-solid and slab-on-dense-liquid models,
modified as mentioned above for the base layer by using appropriate
ratio-based formulas. For all structural layers, nearly 95 percent
of all records screened were labeled with a flag of “0,” or
acceptable, while most of the few remaining nonzero flags were “1,”
or marginal.

Evaluation of the Backcalculated Data Derived from Layered
Elastic Analysis

For the flexible pavement data and for the rigid pavement data
using layered elastic theory (all generated through the MODCOMP
backcalculation program), the screening process produced some data
tables with fairly good agreement between the two analysis methods
and many tables with relatively poor agreement between the back-
and forwardcalculated moduli.

By way of background, for backcalculation involving more than
two unknown layers, in most backcalculation programs, the modulus
values are effectively derived from the bottom up. This factor is
also true for the MODCOMP program. As a result, when a small error
occurs in the lowest unknown layer—the subgrade—the compensating
layer effect will inevitably occur, by alternately under- and
over-estimating the moduli of the succeeding (overlying) layers. In
these cases, by the time the fourth or fifth layer from the bottom
is adjusted through the iteration process—the bound surface
course—the necessary compensation for an incorrect subgrade modulus
has taken place and a reasonable result has generally been obtained
in spite of alternating too-high and too-low results in the
intermediate layers beneath the surface course. The compensating
layer effect appears to be mainly associated with distressed
pavements that usually do not follow the rules and assumptions made
of linear or even nonlinear layered elastic theory. On the other
hand, with homogeneous, undistressed, and well-defined pavement
structures, backcalculation often appears to work quite well. This
observation is especially true for interior slab concrete
tests—although only when a two-unknown layer system is used (plus a
hard layer at some depth, if present).

Accordingly, the backcalculated asphalt and concrete surface
course moduli using MODCOMP resulted in the best correspondence to
the forwardcalculated moduli of all layers analyzed. For the
asphalt moduli, better than 70 percent of the correspondence
screened values (for both the point- and the section-data) were
acceptable (flag = 0). For the concrete moduli at the point data
level using MODCOMP, better than 60 percent of the screened data
using a bonded condition in forwardcalculation were acceptable
(flag = 0), while more than 80 percent of these data were
acceptable assuming an unbonded condition between the PCC surface
and the base course, when compared to the forwardcalculated values
for rigid pavements. At the section level for the concrete modulus
derived from MODCOMP, better than 90 percent of the backcalculated
screened data were acceptable, with a correspondence flag of
“0.”

For the subgrade layer, the correspondence between back- and
forwardcalculated moduli using MODCOMP (both linear and nonlinear)
was somewhat poorer than with the asphalt layer. However, these
results are principally from the methodology, not the correctness
(or lack thereof) of each method. Forwardcalculation uses the
center deflection and the shape of the deflection bowl to
characterize the subgrade stiffness under the load plate to a
finite depth, as defined by the shape of the deflection bowl.
Backcalculation uses one or more of the outer geophones to
characterize the subgrade stiffness at that particular distance
from the load, assuming it will also have the same stiffness under
the load plate. Often this does not appear to be the case—hence,
the compensating layer effect. In other instances, in particular
with concrete or a very stiff AC pavements, a horizontally constant
subgrade modulus appears to be a more reasonable assumption.

Consequently, only about 40 percent of the correspondence
screened records for flexible pavement subgrades were classified as
acceptable (flag = 0). The results of screening the subgrade
section tables as well as the nonlinear version of MODCOMP were
similar. On the other hand, most of the bias between the two
methods was in the same direction—the backcalculated subgrade
moduli from MODCOMP were generally higher than those from
forwardcalculation. For the concrete sections, the correspondence
between the two approaches was somewhat better, with about 50
percent of these being classified as acceptable, with a
correspondence flag = 0. In all unacceptable cases, MODCOMP versus
forwardcalculation produced divergent results that were about
equally divided between marginal, questionable, and unacceptable
(flag = 1, 2, or 3, respectively).

For the base layer using the MODCOMP backcalculation program,
many of the backcalculated moduli (and some of the
forwardcalculated moduli from the use of the Dorman and Metcalf
relationship) were not reasonable according to the broad ranges
given in Table 17. Of the remaining values
that were screened using the correspondence flags, only between 30
and 40 percent of the data resulted in an acceptable flag of “0,”
with the remainder once again divided more or less evenly among
marginal, questionable, and unacceptable (corresponding flags = 1,
2, or 3, respectively).

The Microsoft® Excel spreadsheets containing all
formulae used in phase I of this study have been provided to FHWA,
so all forwardcalculation input quantities are totally transparent
to those who wish to use the methodology, whether for screening or
in rehabilitation design. To this end, four spreadsheets are
available—two for asphalt-bound surfaces (using SI and U.S.
Customary units) and two for cement-bound surfaces (SI and U.S.
Customary). These spreadsheets can be obtained by contacting LTPP
Customer Support Services: by phone at 202– 493–3035 or by e-mail
at ltppinfo@fhwa.dot.gov. A
publication entitled Guidelines for Review and Evaluation of
Backcalculation Results (FHWA-HRT-05-152) is also available
from FHWA for those wishing to use these spreadsheets.

CONCLUSIONS

This report presents the results of a study that used
forwardcalculation techniques to screen the entire set of
backcalculated computed parameter results in the LTPP database. Two
parallel computed parameter data sets now exist: one existing set
resulting from backcalculation and one newly created set resulting
from forwardcalculation, for the same LTPP sections and using the
same FWD input data. This choice does not mean that one method or
the other is strictly right or wrong. They are, however, in many
instances different.

As this report shows, backcalculation is more of an art than a
science, although it is certainly rigorous and scientific in the
sense that it can use the entire deflection basin to fairly
accurately match up the theoretical and actual measured deflections
with backcalculated modulus values. The user, however, must be
aware of its limitations and assumptions, such as
linear-elasticity, homogeneity, isotropic behavior, in addition to
the assumption of being horizontally identical in stiffness for
each structural layer beneath the width of the deflection basin,
especially if a linear-elastic model is chosen for backcalculation.
A skilled backcalculation analyst can deal with these potential
shortfalls quite well by skillfully modeling the pavement system
and by dealing with apparent or actual nonlinearity in a variety of
ways.

For example, the analyst can assign a semirigid layer at some
depth where the deflection basin suggests a possible stiff layer or
bedrock, similar to how the Hogg model in forwardcalculation
defines a depth to an apparent stiff layer, whether there actually
is a very stiff layer or bedrock or not at that depth. Adjacent
structural layers may also be combined to backcalculate an unknown
layer modulus that would otherwise not influence the deflection
basin enough to enable the derivation of a modulus value for a
relatively thin structural layer. In other cases, a single,
relatively thick pavement layer can be separated into two layers in
the input file to characterize the apparent difference in material
response as a function of depth within the pavement.

What would be most satisfying and give considerably more
credibility to both backcalculated and forwardcalculated results is
if they are both reasonable and correspond to one another (within
reason) with a flag of “0” (i.e., within a factor of 1.5 of one
another). For in situ layered-elastic properties of pavement
systems, this level of correspondence can be considered reasonable
and generally satisfactory for engineering purposes. When this
correlation occurs, it can be maintained that the input assumptions
for either approach were essentially correct and that either set of
moduli may be used with confidence.

But what should be done when the correspondence flags between
back- and forwardcalculation are 1, 2, or 3 (i.e., greater than a
factor of 1.5 different from one another)? This situation means
that both values are within a reasonable range according to
Table 17 and are neither fixed nor assumed. It
probably also means that the theoretical assumptions of one or the
other, or both, methods are incorrect—or the method of choice is
not being used wisely or correctly. Although forwardcalculation
produced more stable results, globally, than the three- or
more-layer backcalculation approach (using MODCOMP), backcalculated
values cannot be categorically rejected, because they do offer a
theoretically correct solution to a specific FWD deflection basin,
however implausible they may appear. Accordingly, some of these
cases may well be implausible, but there is still a
possibility—however remote—that the values are in fact
more or less correct, given the nature of in situ pavement
materials and the often bizarre behavior of these materials under a
load and under the influence of ever-changing environmental and
other site-specific factors.

Now, however, the LTPP database user can be forewarned by the
various flags and data quality checks as outlined in this report
and assess whether to accept the values present in the existing
backcalculated database (or the forwardcalculated parallel
database), depending on the intended evaluation purpose.

In conclusion, the slab-on-elastic-solid or slab-on-dense-liquid
models for backcalculation offer excellent correspondence with the
rigid pavement forwardcalculation techniques, with very few values
being labeled unreasonable. Accordingly, in the vast majority of
cases, either (or both) may be used with a good degree of
confidence.

RECOMMENDATIONS

As a remedial measure, it is recommended that the current LTPP
backcalculated tables be retained as is, although with the various
checks and flags added as outlined in this report. It is also
recommended that the forwardcalculated values be appended to the
computed parameter data tables, so that an LTPP database user can
compare the two sets of values obtained from the same deflection
basin. When these pairs of values pass both the reasonableness test
and the acceptable (correspondence flag) test, then either (or
both) may then be used with a greater degree of confidence than one
or the other as a stand-alone value.

Future Analysis of the LTPP FWD Deflection Data—Conduct both
Back- and Forwardcalculation

To date, only a limited percentage of the total volume of FWD
load-deflection data have been processed through either back- or
forwardcalculation. As this report documents, no single truth
exists to determine or quantify actual in situ layered elastic
moduli. The results obtained through backcalculation depend at
least as much on how the program of choice is used than on the
actual mechanics of how the program functions. Although
forwardcalculation produces a unique set of values, these values
are approximations, not cast-in-stone truth or baseline values.
However, these approximations can certainly be used to guide the
backcalculation program user to see if he/she is in the ballpark
with answers obtained through any chosen method of load-deflection
data analysis.

As a QA measure, it is further recommended that the entire FWD
load-deflection database, where back- or forwardcalculation can be
carried out, be reanalyzed in the case of the previously analyzed
MODCOMP data along with the unanalyzed post-1998 data. Furthermore,
since LTPP is a research project, it is not recommended that only
one solution be offered as new or improved LTPP computed
parameters, but rather two or more different solutions be provided
to the LTPP database user. Forward- and backcalculation programs
with different theoretical assumptions (for example, by comparing
MODCOMP and forwardcalculation results) should be employed so that
the LTPP database user can compare the values obtained for the same
layer, test point, and test section.

Especially in the case of layered elastic backcalculation of
three or more unknown layers, it is very important that each test
section be handled on an individual basis by an experienced and
savvy user of the selected backcalculation program. Even for an
experienced analyst, this process will take some time, since each
LTPP section should be carefully reviewed for discrepancies between
the program’s input assumptions and actual deflection behavior. If
MODCOMP (or any other backcalculation program) is selected for a
second round of LTPP deflection data analysis, much more time will
be necessary than for a typical batch processing of load-deflection
data. For any layered elastic analysis using backcalculation,
forwardcalculation as outlined herein may be used as a comparison
and, if desired, to seed the backcalculation routine selected, as
long as the forwardcalculated values are well within the reasonable
ranges in Table 17. This table may be changed
and updated as appropriate, for example by narrowing the range of
reasonable asphalt layer moduli as a function of pavement
temperature (if available), if new in situ modulus information is
forthcoming about any of the materials listed in the table. Seeding
with forwardcalculated values may well positively affect the
backcalculated solutions, providing a more reasonable starting
point for a good deflection basin fit and a more believable set of
moduli in the output.

It will not be necessary to reanalyze or rescreen the back- or
forwardcalculated values in the slab-on-elastic-solid or
slab-on-dense-liquid database, since these two different approaches
produced very similar results. It is recommended that experienced
analysts carry out the same two approaches on the remaining rigid
pavement data measured at interior slab locations using
slab-on-dense-liquid and slab-on-elastic-solid theory for
backcalculation.

It is recommended that a second round of LTPP FWD deflection
data analysis consist of the following steps:

Forwardcalculation of all LTPP sections—Use
the methods as outlined in this report.

Backcalculation of the LTPP rigid pavement
sections—Use slab-on-elastic-solid or slab-on-dense-liquid
foundation analysis, as developed under the previous LTPP
backcalculation project (FHWA-RD-01-113).

Backcalculation of the LTPP flexible pavement
sections—Use a sound and user-friendly layered elastic
backcalculation analysis program and seed values from
forwardcalculation (provided these values are within reasonable
ranges).

Recommended Actions to Improve Future Backcalculation
Results

In the future, the forwardcalculated values can be used in the
following ways to improve the backcalculation results:

The forwardcalculated values (if they are within a reasonable
range) should be used to "seed" most backcalculation routines to
assist in arriving at more reasonable and accurate backcalculated
modulus values.

When a "flag" arises for any reason (reasonable ranges, large
discrepancies with forwardcalculation, etc.), at the discretion of
the analyst backcalculation can be modified and repeated to
minimize these differences and/or mitigate the compensating layer
effect, thereby improving the backcalculated database while leaving
the forwardcalculated results in the database as well.

Notes on a Viable Alternative to Classic Multilayered Elastic
Backcalculation

This section is based primarily on the knowledge and experience
of the investigators of this task order, not an evaluation outcome
of the project.

As an alternative to classic, multilayered backcalculation
(e.g., MODCOMP, MODULUS, EVERCALC, etc.), some LTPP database
processing time could be saved by using the proprietary ELMOD
program, which is easier for a hands-off batch mode. This technique
would still provide LTPP database users with the results of two
different approaches using two methods (backcalculation with ELMOD
and forwardcalculation as developed for this project) that are
similar in some respects and dissimilar in others. The current
version of ELMOD offers the user two internal processing
engines—one using a deflection basin matching routine similar to
traditional backcalculation and the other using the radius of
curvature method, which is similar to the forwardcalculation
routine for bound surface layers presented in this report. Based on
our experience with ELMOD, the latter is more stable, and therefore
more believable, because in many cases, layered elastic pavement
systems (especially distressed pavement sections) generally do not
follow the classical laws of homogeneity, isotropic properties, and
horizontally constant moduli. Accordingly, both ELMOD approaches
should be batch-processed so as to provide the LTPP database user
with three comparable solutions—two from ELMOD and one from
forwardcalculation. Traditional backcalculation (for example, using
MODCOMP again) could also be added as a fourth set of values, as
long as they are carried out more carefully and thoroughly than
before, as mentioned previously.

The suggestion to consider the use of ELMOD, above, does not
necessarily mean that ELMOD is better or more accurate than
MODCOMP, EVERCALC, or MODULUS, etc. All of these traditional
programs—as well as ELMOD and the forwardcalculation techniques
presented in this report—produce approximations of in situ modulus
values, at best. When using elastic layered theory on the vast
quantity of LTPP data, ELMOD as a backcalculation engine would be
both less costly and more efficient than most other backcalculation
approaches known to the research team.

There may well be a public domain or other alternative to ELMOD,
but the research team is not familiar with such an alternative. As
far as is known, ELMOD is the only program that will both run
deflection basin matching and radius of curvature or a similar
method in one package.